Results of Case 1 - Steel Building Benchmark Study

EXTRACTION OF SECOND ORDER SYSTEM MATRICES FROMSTATE-SPACE REALIZATIONS1 2Dionisio Bernal , Burcu Gunes1 2 Associate Professor, Graduate StudentDepartment of Civil and Environmental Engineering, 427 Snell Engineering Center,Northeastern University, Boston MA 02115, U.S.A1 2 bernal@neu.edu, bvuran@lynx.neu.eduIntroductionThe last two decades have seen the development of robust algorithms to constructminimum order state-space realizations from input/output data (Juang and Papa, 1984).When expressed in modal coordinates these realizations provide n pairs of complexeigenvalues and eigenvectors that can be related to the system’s natural frequencies anddamping ratios and to the values of the system modes at the sensor locations. Modelupdate algorithms typically utilize identified modal parameters, instead of the physicallymeasured response, as the targets to be matched in fitting a model to the data. Deviationsin optimum model parameters for data collected at different times is often used to inferdamage. An important difficulty in a model-update damage identification strategy is thefact that the formulation becomes ill-conditioned when the “free parameter” space islarge in comparison to the number of constraints imposed by the available data. One wayto ameliorate the problem is to delay the introduction of a class of model into the processby focusing on changes in system matrices obtained directly from the measured data. Weuse the term delay to ...